Abstract:

Although galaxies were suggested and dismissed as potentially useful
cosmological tools decades ago, it is time to revisit this potential in
the light of high resolution observations using HST. It was recognized
early in the development of HST that imaging surveys would be very
fruitful in unraveling the evolution of the galaxy populations, and
perhaps a well-behaved population such as the ellipticals may indeed be
useful for cosmological purposes. This paper summarizes what we have
learned thus far, and explores the use of serendipitously discovered
gravitational lenses for the measurement of the cosmological constant
. The application of HST to the measurement of the Hubble
constant was planned, but the application to cosmological parameters has
perhaps been more surprising, bearing in mind that we are only two years
past the refurbishment Shuttle mission which restored HST to full
potential. We are clearly just beginning to tap the full potential of
HST for cosmological problems.

First, WFPC2 on HST has provided the means to make rapid progress
towards solving a long-standing problem in observational cosmology,
viz. the nature of the objects contributing to the faint blue galaxy
counts. The solution to this problem has been found in the increasing
number of irregular and peculiar systems seen as HST probes to
greater depths.
Galaxies in the Medium Deep Survey (MDS) have been reliably classified
to magnitudes in the F814W band, at a mean
redshift 0.5. A high proportion (40%) of these
objects are irregular or anomalous and they have great diversity. They
include compact galaxies, galaxies or protogalaxies with superluminous
starforming regions, interacting pairs, and diffuse low surface
brightness galaxies of various forms. These diverse objects contribute
most of the excess counts in the I-band at our limiting magnitude, and
when MDS images with BVI data are taken into account, they also explain
most of the `faint blue galaxy' excess. Of the irregular population
(40% of the total at I=22), about 30% show multiple, high surface
brightness components indicative of starburst activity.

But roughly half of the faint galaxies (I < 22) appear to be similar to
regular Hubble-sequence examples observed at low redshift, with relative
numbers of spheroidal and disk systems roughly consistent with nearby
samples, indicating that the bulk of the local giant galaxy population
was in place at half the Hubble time. Moreover, the giant population has
certainly faded since z = 1, by about 1 mag. for the E/S0s and about the
same for the early-type spirals. For the first time, we have observed
directly the evolution of the luminosity function of E/S0 galaxies.
We have found evidence for weak gravitational shear in the vicinity of
E/S0 field galaxies, and have used this effect to constrain their masses
and the cut-off radii of their dark matter halos.

The ``major'' merger rate has evolved only slowly with look-back time,
as out to z = 1 or 1.5, although there is already evidence
from the deeper surveys that the rate may have been greater at higher
redshifts. ``Major'' merging is probably not a major component of the
explanation for the faint blue galaxy excess (to I = 22. ``Minor
merging'' is a different story, and more difficult to address
observationally. The deeper HST surveys, addressing the redshift range
from 1 to 2, show increasing evidence of ``conglomerations'',
i.e., groupings of what appear to be sub-galactic `clumps'.

The clear picture which has thus emerged from the HST MDS
is one in which the giant ellipticals and spirals have passively
faded but have otherwise been relatively stable since z = 1, whereas
there has been rapid evolution of the irregular/peculiar galaxy population --
about 20% of them were brighter by about 2 mags. only 6Gyr. ago. This
latter population is not at all homogeneous, however, and seems to
comprise galaxies in formation as well as fading dwarf irregulars.

Finally, and perhaps of greatest interest to this conference, strong
gravitational lenses in MDS and archival data have included the first
examples of HST-discovered ``Einstein crosses'' centered on elliptical
galaxies. These can be used to measure : combining HST with
published data, our results show that if
. We can exclude the model at the
95 % confidence level. We also find that an open universe is less
likely by a factor of about 5--10 than a flat universe with non-zero
.

Although it was hoped that galaxies would provide some clues to the
shape of the universe (Sandage 1961) these hopes were dashed when Tinsley
(1968) and coworkers pointed out that the galaxies must surely have
evolved to their present numbers, shapes and sizes. Before the advent of
HST, ground-based imaging could not be used to separate the galaxy
populations, but now we have an instrument which can, and we can see how
they have evolved individually. If we look at the total galaxy number
counts, for example, then the effect of cosmological geometry, e.g., a
range in the value of from 0 to 1, has an effect which is
smaller than the differential between blue and red galaxy counts at B =
24 (Broadhurst, Ellis & Glazebrook 1992,
Metcalfe et al. 1995, Colless et al. 1994, Koo & Kron 1992, Lilly
et al. 1993). The identification of this blue population was thus of
paramount importance in order to separate and remove it as a
`contaminant' to the problem of world geometry. Having done this, we may
then be in a position to use a more well-behaved galaxy species, the
ellipticals (if we can show that they formed at high redshift), in order
to constrain the geometrical parameters. In order to make progress on
these problems, we clearly needed large samples. Although the field of
view of HST is small, the opportunity presented itself to take pictures
of random fields with the Wide Field and Planetary Camera (WFPC2) when
another HST instrument was targeted towards a known object of interest.

The Medium Deep Survey (MDS) is the HST Key Project which uses these
parallel observations of random fields taken with WFPC2 in broad-band
filters. Primarily, and for pointings of only a few orbits, exposures
are taken in V and I; but for the longer pointings of six orbits or
more, the B-band has been given priority, especially in HST observing
cycles 4 and 5, when the scheduling system became more
sophisticated. The overall goals are wide-ranging, but they are all
based on statistical studies of the properties of a large sample of
faint galaxies, as well as Galactic star counts and studies within
nearby extragalactic objects. In particular, the Survey was designed to
resolve the problem of the abundant population of faint blue galaxies.

Typical MDS observations range from 600 to 2000 seconds per exposure,
and may consist of 1--20 exposures of the same field.
In Cycles 1--3, 146 fields were observed with the WFC in a total exposure
time of 240 hours. To December 1995, Cycle 4/5 MDS observations had
been made in nearly 400 fields, with a total of 400 hours in the two
predominant filters: F606W, somewhat redder and broader than Johnson V
, and F814W, close to Kron-Cousins I . Of these fields, 140 were
exposed to both filters, and over 30 had at least three exposures in
each. Eight fields had exposures in the BVI set. The filters have been
chosen to maximize the sensitivity for typical galaxies at intermediate
redshifts ().
A typical WFPC2
MDS field contains 50--400 detectable sources within the Wide Field
Camera (WFC) to a limiting magnitude of = 24--26 depending on
the total exposure. The precision with which morphological properties
can be measured is, of course, a function of both angular size and
apparent magnitude.

The results of morphological typing into three crude galaxy classes
(E/S0, early-type spirals and late-type spirals/irregulars) has been
described by Abraham et al. (1996), and summarized by Longair (these
Proceedings).

The mild-evolution models (e.g., Guiderdoni & Rocca-Volmerange 1990)
predict luminous galaxies of large angular size at high redshift: such
objects are certainly seen in the data, consistent with a brightening at
higher redshift. Still, the excess number counts, at least to I = 22,
are largely unexplained by `giant' spirals or ellipticals, which are
observed to have only passive (luminosity) evolution. Their number
counts (Glazebrook et al. 1995, Driver et al. 1995b, Abraham et al. 1996),
size vs. redshift relationship (Mutz et al. 1994), and structural
parameters (Windhorst et al. 1994, Phillips et al. 1995, Forbes et
al. 1995,1996) all indicate a relatively benign population: the bulk of the
local giant population was apparently in place at half the Hubble time.

Perhaps the easiest galaxy type to separate out from the general
population is the E/S0s. The automated galaxy classification software
developed for the MDS and based on the maximum likelihood method
(Ratnatunga et al. 1994a) allows us to select galaxies which have the
`de Vaucouleurs' profile. We have thus constructed the
luminosity functions of elliptical galaxies using data from the MDS
together with archived HST surveys (Groth et al. 1994, with spectroscopy
from Lilly et al. 1995). Photometric redshifts of these E/S0s have been
determined using V-I colors and sizes to an accuracy of up
to , and checked with MDS follow-up spectroscopy or published
values (Lilly et al. 1995) for about 10% of the sample. The
luminosity functions, constructed in 3 different redshift bins (, , ) are shown in Fig.1 (from Im et
al. 1996b).

These independent luminosity functions show the brightening in the
luminosity of E/S0s by about magnitude at , and no
sign of significant number evolution. This is the first direct
measurement of the luminosity evolution of E/S0 galaxies, and our
results support the hypothesis of a high redshift of formation (z >>
1) for elliptical galaxies, together with weak evolution of the major
merger rate at z < 1. The high redshift of formation is consistent
with that of cluster ellipticals (Bower et al. 1992, Ellis 1996) as
determined from the small scatter in the (U-V) colors, and with HST studies
of ellipticals in high redshift clusters (Dickinson et al. 1995). The
stars in ellipticals are as old as those in globular clusters.

The majority of ellipticals must have formed at z >> 1, and
their number evolution was not significant at z < 1. Our data are
consistent with a merger rate of Gyr for the
model, and Gyr for the model with
and with no strong major merger rate evolution
(§ 3).

Given the negligible number evolution, the observed color distribution
of ellipticals can be matched with the predictions of stellar synthesis
models. The observed V -I color distribution for I < 22 requires
evolution in the spectral energy distribution (SED), otherwise there is
an excess of very red ellipticals with respect to the prediction of the
no-evolution (NE) model (Im et al. 1996a). Luminosity evolution models
based on a single starburst at the redshift of formation
(if ) or (if ) can
comfortably match the observed color distribution, suggesting that most
ellipticals are neither very young nor very old ( 9 < age < 20Gyr). We have used the number-magnitude counts in an attempt to
constrain not only the evolution of ellipticals, but also the
cosmological parameters or . Our results favor low
or non-zero models for a minimal (local) merger rate.
The use of the E/S0s to constrain the cosmological parameters is stymied
by two problems, however: (i) the uncertainty in the faint-end slope of
the luminosity function of these galaxies, and (ii) the uncertainty in
the actual epoch or range of epoch of formation. To see how we may
better exploit the elliptical population to measure , see
§ 5.

Statistical properties of galaxies are measured to I = 24 with
WF/PC and 25 with WFPC2.
For the pre-refurbishment WF/PC images, the structural parameters of
about 13,000 objects are presented by Casertano et al. (1995), using
data taken from about 112 fields. Sizes, magnitudes, colors and crude
classifications are based on two-dimensional model fitting to
undeconvolved images (Ratnatunga et al. 1994a). Number counts in the
range 18<I<22 exceed the ground-based numbers by about 50%, a range
over which many ground-based objects may have been misclassified as
stars. The ellipticals become redder for mag, but the
spirals show no trend of apparent color with magnitude, indicating that
they are intrinsically slightly bluer at higher redshift when
K-corrections are taken into account. For galaxies with in
WFPC2 data, the maximum-likelihood fits have been found for combined
disk-plus-bulge models of all galaxies.

The angular size distribution certainly favors a steep luminosity
function, but the faint data also demonstrate that the numbers of
galaxies with both blue () colors and moderately large at ) angular sizes
exceed the non-evolving predictions by a factor of two, and are in good
agreement with the simple pure luminosity evolution model (Roche et
al. 1996a). This model incorporates the steep luminosity function
() for later-type galaxies and moderate luminosity
evolution (-- at ) for spiral
galaxies of all luminosities (similar to the models of Campos & Shanks
1996).

The excess of large blue galaxies in the deeper fields (fig. 2) is positive
reinforcement of our finding that large, spiral galaxies do
undergo significant luminosity evolution to , and that
evolutionary brightening is not confined to dwarf galaxies. This
interpretation is supported by the spectroscopic results of Schade et
al. (1995), Lilly et al. (1995) and Forbes et al. (1996), all of which
suggest a similar brightening of spirals with redshift.

Figure:V-I color distributions for small
and large galaxies---from Roche et al. (1996a)

Another important scientific aim of the MDS is to identify possible AGN
candidates from the images in order to measure the faint end of the AGN
luminosity function as well as to study the host galaxies of AGNs and
nuclear starburst systems. We are able to identify candidate objects
based on morphology: candidates are selected by fitting a combined bulge
and disk model to the galaxy and examining the residual once this model
image is subtracted. Each candidate exhibits an unresolved point source
in the nucleus which is well fit with a stellar point spread function.
We have discovered that there is a population of unresolved nuclei
within those galaxies fitted simultaneously with disk and bulge
components ( 22); these galaxies show narrow emission
lines in the spectroscopic follow-up program. HST photometry indicates
that these stellar nuclei have the colors of moderately redshifted
Seyfert I galaxies. About 6% of field galaxies at may,
therefore, contain AGN which are 3--4 magnitudes fainter than the host
galaxies (Sarajedini et al. 1996).

Figure: Nearest-neighbor pair counts versus angular separation,
, normalized by random sample statistics. The curves show the
expected numbers of pairs for the given evolution in the merger rate,
assumed to take the form .

Down to 25 mag the number of galaxy pairs with separations
3 0 is consistent with the inward extrapolation of the
angular two-point correlation function
observed from the same data (fig. 3); the fraction of such
pairs showing morphological evidence for physical association accounts
for two-thirds of the amount indicated by ) . Moreover, relative to
field galaxies, the (V-I) color and I-magnitude difference
distributions of 3 0 pairs are similar.

We find that merging has a moderate dependence on redshift: we estimate
the rate of merging
, with for galaxies with 25
mag. (fig. 4). There are two models consistent with these data: (a) a
low density universe with strong clustering evolution parameterized by a
clustering exponent 1.0; or (b) two galaxy populations
identified by their clustering properties, in which the more weakly
clustered population fades or dissipates but does not take part in
widespread merging prior to z.3, whereas the more strongly
clustered population, which we associate with local ellipticals and
disks within two magnitudes of , takes part in minor mergers with
dwarf galaxies at the uniform merging rate observed locally, out to
1.0.

The WFPC2 images are ideal for weak lensing studies, since ellipticities and
position angles can be measured routinely to I = 24 in the summed
exposures. There is indeed evidence for `weak shear' lensing (Griffiths
et al. 1996), as evidenced by the preferential orientation of background
field galaxies (I = 22--24), in the vicinity of foreground ellipticals
(I = 18--22). The shear cause the background galaxies to be
preferentially oriented in the direction perpendicular to the radius
vector to the foreground galaxy, and is detected as a deviation of the
distribution of the position angle from uniformity (see
fig. 5).

Figure: Weak lensing signal for foreground ellipticals,
spirals and the control sample of stars, using a Fourier-series
decomposition.

For the rest of the foreground galaxies (mostly spirals), the observed
signal is considerably weaker. This is an expected trend because the
late-type galaxies have less mass and shallower profile near the center
than ellipticals. But again we find that the observed signal is well
matched by the isothermal sphere model with . No
signal is observed in a control sample with stars as ``foreground''
objects.

In the process of visual examination of a sample of elliptical galaxies
selected by the automated MDS data processing, we discovered a few of
the `Einstein cross' type of gravitational lenses in archived and MDS
data. Such objects would not have been discovered in ground-based data
because of the required resolution. These are the first lenses centered
on relatively bright elliptical galaxies with well understood
properties. As shown in Im et al. (1996c), such objects may eventually
be powerful cosmological tools.
In order to combine the information on cosmological parameters
from all available lenses, we constructed a likelihood function which is
a product of the probability of each lens having the observed
given , , and the cosmological parameters.
Gravitational lenses were selected using the following criteria:
1) The strong lensing must be caused by a single galaxy lens. For example,
we do not include 0957+561 in our sample since there are two lensing
galaxies in this system,
2) The apparent magnitude and the redshift of the lens galaxy must be
known or estimated to reasonable accuracies. Accurate values for
and are important for estimates of the dynamical properties of the
lens galaxy.
3) It must be established that the lens galaxy is an elliptical.
For example, we do not include MG0218+0357 in our study since there is
good evidence that the lensing galaxy is a spiral or a late-type galaxy
4) For lens candidates that do not have a measured value for ,
we select only those which show distinctive features such
as rings or crosses.

We find that there are seven strong gravitational lenses that meet these
selection criteria in the MDS and published literature (Im et
al. 1996c). In fig. 6, we present the likelihood function in
- space, with contours of various levels of statistical
significance. The likelihood function peaks at with
low . The diagonal line represents the case when
. If , then the model
is strongly excluded at a confidence level >95 %. The low
model with is excluded at weaker statistical significance
(80--90%).

Figure: The maximum likelihood value for using strong
gravitational lenses (elliptical galaxies) from HST and published data

The ``excess number counts'' above the predictions of no-evolution
models are caused largely by the evolution of low-luminosity systems,
which have a higher space density than that predicted from local
ground-based surveys. These objects manifest themselves as large
numbers of irregular galaxies in the data, a large fraction of which
seem to have multiple starburst components. At the faint end of the
survey, an increasing frequency of irregular systems and conglomerations
are seen, including what appear to be high redshift galaxies or
protogalaxies in various stages of formation and evolution.

Early-type galaxies are seen to undergo luminosity evolution and were
brighter by about 1 mag. at z = 1. Their numbers and sizes are
consistent with a high redshift of formation, z >> 1.
Nevertheless, it is difficult to use them to probe the cosmological
parameters because of two problems: (i) the faint end slope of the
LF for these galaxies is not well determined, and (ii) the actual
epoch of formation is unknown. Although the observations support a
low value for , this result is tentative.

The rate of galaxy merging has not evolved rapidly since z = 1, in
contrast with several claims. However, the deeper HST surveys may
already indicate that the merger rate was much higher at z between 1 and
3 than it was at z < 1.

Serendipitously discovered strong gravitational lenses may eventually
provide one of the best measures of . These
objects are found at the rate of several per square degree, but
require the angular resolution of HST, together with follow-up spectroscopy
with 10m-class ground-based telescopes.